Hufton Peter G, Lin Yen Ting, Galla Tobias
Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.
Center for Nonlinear Studies and Theoretical and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev E. 2019 Mar;99(3-1):032121. doi: 10.1103/PhysRevE.99.032121.
We study classical Markovian stochastic systems with discrete states, coupled to randomly switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of infinite timescale separation. We show that this can lead to master equations with bursting events. Negative transition rates can result in the reduced master equation, leading to unphysical short-time behavior. However, the reduced master equation can describe stationary states better than a leading-order adiabatic calculation, similar to what is known for Kramers-Moyal expansions in the context of the Pawula theorem [R. F. Pawula, Phys. Rev. 162, 186 (1967)PHRVAO0031-899X10.1103/PhysRev.162.186; H. Risken and H. Vollmer, Z. Phys. B 35, 313 (1979)ZPBBDJ0340-224X10.1007/BF01319854]. We provide an interpretation of the reduced dynamics in discrete time and a criterion for the occurrence of negative rates for systems with two environmental states.
我们研究具有离散状态的经典马尔可夫随机系统，该系统与随机切换的外部环境相耦合。对于快速的环境过程，我们推导了系统本身的约化动力学，重点关注对无限时间尺度分离的绝热极限的修正。我们表明，这可能会导致出现具有突发事件的主方程。负跃迁速率可能会出现在约化主方程中，从而导致不符合物理实际的短时间行为。然而，与帕乌拉定理[R. F. 帕乌拉，《物理评论》162, 186 (美国物理学会，1967年)；H. 里斯肯和H. 福尔默，《物理学报B》35, 313 (德国施普林格出版社，1979年)]背景下的克拉默斯 - 莫亚尔展开类似，约化主方程能够比领先阶绝热计算更好地描述稳态。我们给出了离散时间下约化动力学的一种解释，以及具有两个环境状态的系统出现负速率的一个判据。
